Lump-type solutions of a generalized Kadomtsev-Petviashvili equation in (3+1)-dimensions

doi:10.1088/1674-1056/ab3f20

中国物理B ›› 2019, Vol. 28 ›› Issue (10): 100203-100203.doi: 10.1088/1674-1056/ab3f20

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

Lump-type solutions of a generalized Kadomtsev-Petviashvili equation in (3+1)-dimensions

Xue-Ping Cheng(程雪苹), Wen-Xiu Ma(马文秀), Yun-Qing Yang(杨云青)

1 Physics, Mathematics, and Information College of Zhejiang Ocean University, Zhoushan 316004, China;
2 Key Laboratory of Oceanographic Big Data Mining & Application of Zhejiang Province, Zhoushan 316022, China;
3 Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA;
4 Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;
5 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;
6 International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa

收稿日期:2019-04-09 修回日期:2019-08-07 出版日期:2019-10-05 发布日期:2019-10-05
通讯作者: Xue-Ping Cheng E-mail:chengxp2005@126.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11505154, 11605156, 11775146, and 11975204), the Zhejiang Provincial Natural Science Foundation of China (Grant Nos. LQ16A010003 and LY19A050003), the China Scholarship Council (Grant No. 201708330479), the Foundation for Doctoral Program of Zhejiang Ocean University (Grant No. Q1511), the Natural Science Foundation (Grant No. DMS-1664561), the Distinguished Professorships by Shanghai University of Electric Power (China), North-West University (South Africa), and King Abdulaziz University (Saudi Arabia).

Lump-type solutions of a generalized Kadomtsev-Petviashvili equation in (3+1)-dimensions

Xue-Ping Cheng(程雪苹)^1,2, Wen-Xiu Ma(马文秀)^3,4,5,6, Yun-Qing Yang(杨云青)^1,2

1 Physics, Mathematics, and Information College of Zhejiang Ocean University, Zhoushan 316004, China;
2 Key Laboratory of Oceanographic Big Data Mining & Application of Zhejiang Province, Zhoushan 316022, China;
3 Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA;
4 Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;
5 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;
6 International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa

Received:2019-04-09 Revised:2019-08-07 Online:2019-10-05 Published:2019-10-05
Contact: Xue-Ping Cheng E-mail:chengxp2005@126.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11505154, 11605156, 11775146, and 11975204), the Zhejiang Provincial Natural Science Foundation of China (Grant Nos. LQ16A010003 and LY19A050003), the China Scholarship Council (Grant No. 201708330479), the Foundation for Doctoral Program of Zhejiang Ocean University (Grant No. Q1511), the Natural Science Foundation (Grant No. DMS-1664561), the Distinguished Professorships by Shanghai University of Electric Power (China), North-West University (South Africa), and King Abdulaziz University (Saudi Arabia).

摘要/Abstract

摘要： Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation in three cases of the coefficients in the equation. Then the sufficient and necessary conditions to guarantee the analyticity of the resulting lump-type solutions (or the positivity of the corresponding quadratic solutions to the associated bilinear equation) are discussed. To illustrate the generality of the obtained solutions, two concrete lump-type solutions are explicitly presented, and to analyze the dynamic behaviors of the solutions specifically, the three-dimensional plots and contour profiles of these two lump-type solutions with particular choices of the involved free parameters are well displayed.

关键词: lump-type solution, generalized (3+1)-dimensional Kadomtsev-Petviashvili equation, Hirota bilinear form, symbolic computation

Abstract: Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation in three cases of the coefficients in the equation. Then the sufficient and necessary conditions to guarantee the analyticity of the resulting lump-type solutions (or the positivity of the corresponding quadratic solutions to the associated bilinear equation) are discussed. To illustrate the generality of the obtained solutions, two concrete lump-type solutions are explicitly presented, and to analyze the dynamic behaviors of the solutions specifically, the three-dimensional plots and contour profiles of these two lump-type solutions with particular choices of the involved free parameters are well displayed.

Key words: lump-type solution, generalized (3+1)-dimensional Kadomtsev-Petviashvili equation, Hirota bilinear form, symbolic computation

中图分类号: (Partial differential equations)

02.30.Jr

02.70.Wz (Symbolic computation (computer algebra)) 02.60.Cb (Numerical simulation; solution of equations)

程雪苹, 马文秀, 杨云青. Lump-type solutions of a generalized Kadomtsev-Petviashvili equation in (3+1)-dimensions[J]. 中国物理B, 2019, 28(10): 100203-100203.

Xue-Ping Cheng(程雪苹), Wen-Xiu Ma(马文秀), Yun-Qing Yang(杨云青). Lump-type solutions of a generalized Kadomtsev-Petviashvili equation in (3+1)-dimensions[J]. Chin. Phys. B, 2019, 28(10): 100203-100203.

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Lump-type solutions of a generalized Kadomtsev-Petviashvili equation in (3+1)-dimensions

Lump-type solutions of a generalized Kadomtsev-Petviashvili equation in (3+1)-dimensions

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